Chapter 13, Problem 16MCQ

To determine

To find: Whether each triangle has no solution, one solution or two solutions.

Answer to Problem 16MCQ

There is no solution

Explanation of Solution

Given information:

  $\begin{array}{l}A={65}^0\\ a=5\\ b=7\end{array}$

Given

  $\begin{array}{l}A={65}^0\\ a=5\\ b=7\end{array}$

Here $A={65}^0$ is Acute angle.

Because A is Acute and $5<7$ that is $a<b$

Now we need to find $h$ and compare it to $a$ .

We know

  $h=b\sin A$

On substituting values

We get

  $\begin{array}{l}h=b\sin A\\ \Rightarrow h=7\sin \left({65}^0\right)\\ \Rightarrow h=7\left(0.906\right)\\ \Rightarrow h=6.4\end{array}$

Therefore,

We got $a<h$

It means there will be no Solution.

Therefore,

There is no solution.